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# Applied and Computational Mathematics

DMS Applied Mathematics Seminar
Oct 20, 2017 02:00 PM
Parker Hall 328

We are fortunate to have Professor Ming-Jun Lai <http://alpha.math.uga.edu/%7Emjlai/> from the University of Georgia to speak on the topic of matrix completion <https://en.wikipedia.org/wiki/Matrix_completion>.

Title: On Recent Development of Matrix Completion.

Abstract:  I shall first introduce the research on matrix completion based on Netflix problem. Then I will survey some classic methods based on various approaches. In particular, I will explain some recent approaches based on alternating minimization methods including least squares, steepest descent, and Riemann gradient descent techniques. Finally, I shall explain our method of Alternating Projection Algorithm and present a convergence analysis under some conditions. Linear convergence will be shown under a sufficient condition. I will end my talk with numerical experimental results to demonstrate our method is excellent in completing a matrix of low rank.

DMS Applied Mathematics Seminar
Oct 06, 2017 02:00 PM
Parker Hall 328

Speaker: Prof. Xu Zhang, Mississippi State University

Title: Immersed Finite Element Methods for Interface Problems (Basic idea, Development, Analysis, and Applications)

Abstract: Simulating a multi-scale/multi-physics phenomenon often involves a domain consisting of different materials. This often leads to the so-called interface problems of partial differential equations. Classical finite elements methods can solve interface problems satisfactorily if the mesh is aligned with interfaces; otherwise the convergence could be impaired. Immersed finite element (IFE) methods, on the other hand, allow the interface to be embedded in elements, so that Cartesian meshes can be used for problems with non-trivial interface geometry.

In this talk, we start with an introduction about the basic ideas of IFE methods for the second-order elliptic equation. We will present challenges of conventional IFE methods, and introduce some recent advances in designing more accurate and robust IFE schemes. Both a priori and a posteriori error estimation will be presented. Finally, we will demonstrate how IFE methods can be applied to more complicated interface model problems.

DMS Applied Mathematics Seminar
Sep 22, 2017 02:00 PM
Parker Hall 328

Speaker: Hans-Werner van Wyk

Title: Clenshaw-Curtis Type Rules for Statistical Integrals

Abstract: In statistics, many commonly encountered quantities take the form of density weighted integrals. This talk treats their numerical estimation within the Chebyshev approximation framework. In particular, we discuss how a generic one dimensional density function can be incorporated into the construction of Clenshaw-Curtis type quadrature rules, either through an adjustment of the quadrature weights or by generating a set of quadrature nodes that satisfies the optimal spacing property in terms of the density-weighted uniform error. We consider a variety of density functions, including those that are piecewise continuous, or have unbounded support. The accompanying numerical experiments illustrate the behavior and performance of the resulting quadrature rules and offer a comparison with a variety of existing approaches for estimating density weighted integrals.

Applied Mathematics Seminar/Colloquium Yuesheng Xu
Feb 10, 2017 02:00 PM
Parker Hall 250

Speaker: Professor Yuesheng Xu  (Sun Yat Sen University, China)

Title: Mathematics in Data Science

Abstract: We shall discuss several mathematical problems crucial in data science. They include representation of data, mathematical models of recovering a fact from raw data, matching learning and solving optimization problems in data analysis.

Faculty host:  Yanzhao Cao

Applied Mathematics Seminar
Jan 27, 2017 02:00 PM
Parker Hall 328

Speaker:  Dr. Yi Wang,   Professor and Chair at Auburn University at Montgomery (AUM).

Title: Sparse representation with non-linear Fourier atoms

Abstract: In this talk, we study the sparse representation of a finite energy signal with intrinsic mode functions in a dictionary consisting of non-linear Fourier atoms. Each non-linear Fourier atom is a mono-component with a physically meaningful non-negative instantaneous frequency. The sparse representation is obtained adaptively by an orthogonal matching pursuit using a two-level greedy search. It is demonstrated that the representation has efficient energy decay in error compared to the Fourier expansion and wavelet expansion.

Keywords: sparse representation, non-liner Fourier atom, orthogonal matching pursuit, trust-region-reflective search.

Applied Mathematics Seminar
Nov 11, 2016 02:00 PM
Parker Hall 228

Speaker: Dr. Habib Najm.  Habib is a distinguished member of the technical staff at Sandia National Lab. He is also our affiliated  faulty.

Title: Parameter Estimation with Missing Data

Abstract:  Uncertainty quantification on model predictions, using probabilistic methods, requires a full probabilistic specification, e.g., the joint density, for model parameters. Most commonly, only limited information, such as nominal values and error bar is available on model parameters or relevant data. In this talk, I will discuss means for handling this situation, to allow construction of a joint density on model parameters that is consistent with available information, in the absence of raw data. The method will be illustrated in the context of estimation of the joint density on Arrhenius chemical rate coefficients.
Applied Mathematics Seminar
Oct 28, 2016 02:00 PM
Parker Hall 328

Speaker: Hans-Werner van Wyk

Title: A novel finite difference method for the fractional Laplacian

Abstract: In this talk we discuss a novel finite difference method to discretize the fractional Laplacian operator over a bounded domain. Our approach is based on splitting the hypersingular kernel function in its integral representation into two parts, allowing some of the singularity to be absorbed by the operator’s input function $$u$$. We then approximate the resulting weakly singular integral by a weighted trapezoidal rule. Our method is simple to implement and has a higher accuracy than the existing finite difference approximations. For smooth enough $$u$$ and a judicious choice of the splitting parameter, we obtain second order accuracy, uniformly for any diffusion order.

Applied Math Seminar
Sep 30, 2016 02:00 PM
Parker Hall 328

Speaker: Tahir Bachar Issa  (a Ph.D student whose advisor is Professor Wenxian Shen)

Title:  Dynamics in chemotaxis models of parabolic-elliptic type on bounded domain with time and space dependent logistic sources

Abstract: In this talk, we consider the dynamics of a chemotaxis model of parabolic-elliptic type with local as well as nonlocal time and space dependent logistic source on bounded domain. We first prove the local existence and uniqueness of classical solutions for various initial functions. Next, under some conditions on the coefficients, the chemotatic sensitivity and the dimension of the space, we prove the global existence and boundedness of classical solutions with given nonnegative initial function . Then, under the same conditions for the global existence, we show that the system has an entire positive classical solution. Moreover, if the coefficients are periodic in time or are independent of time, then the system has a time periodic positive solution with same period as the coefficients or a steady state positive solution. Furthermore, if the coefficients are spatially homogeneous, then the system has a spatially homogeneous entire positive solution. Finally, under some further assumptions, we prove that the system has a unique entire positive solution which is globally stable. Moreover, if the coefficients are periodic or almost periodic in time, then the unique entire positive solution is also periodic or almost periodic in time.</>

Applied Mathematics Seminar
Sep 14, 2016 02:00 PM
Parker Hall 322

Speaker: Professor Xiaolong Hu, Florida State University

Title:  On mathematical modeling of saltwater intrusion problems

Please note special date, time, and location

Applied Mathematics Seminar
Sep 09, 2016 02:00 PM
Parker Hall 328

Speaker: Dr. Lijin Wang

Lijin is an associate professor at University of Chinese Academy of Sciences. She is currently a visiting scholar at our department.

Title: Modified equations for weakly convergent stochastic symplectic numerical methods via their generating functions

Abstract: In this talk, an approach of constructing stochastic modified equations of weak $$k+k' (k' ≥ 1)$$ order apart from the k-th order weakly convergent stochastic symplectic numerical methods is introduced, using their  underlying generating functions This approach is valid for stochastic Hamiltonian systems with additive noises or multiplicative noises when the Hamiltonian functions $$Hr (p, q), r ≥ 1$$, associated to the diffusion parts depend only on $$p$$ or $$q$$. We will show that the established modified equations are perturbed stochastic Hamiltonian systems of the original systems.

Applied Mathematics Seminar
Sep 02, 2016 02:00 PM
Parker Hall 328

Speaker: Rachidi  Salako

Title:  Global existence and asymptotic behavior of classical solutions to a parabolic-elliptic chemotaxis system with logistic source on $$R^N$$

Abstract: Keller-Segel equations are used to illustrate the time evolution of mobile species toward the gradient of a chemical substance. Such systems are referred  to as chemotaxis systems. Considering the classical Keller-Segel Parabolic-Elliptic/Parabolic chemotaxis systems, in the absence of logistic source, it is known that finite-time blow up of nonnegative solutions can occur when the spatial dimension is greater or equal to 2, but never occurs in the case that the spatial dimension is equal to 1.  In this talk, we consider a Parabolic-Elliptic chemotaxis system with logistic source and prove (i) Local /Global existence of classical solution for various nonnegative initial functions, (ii) Asymptotic behavior of classical solutions. We shall also discuss about some ongoing works about the existence of front propagation and spreading speeds.

Last Updated: 09/25/2015